Finite Element Modeling for Thermal Stresses Developed in Riveted and Rivet-Bonded Joints

Transcription

1 International Journal of Engineering & Technology IJET-IJENS Vol: 11 No: Finite Element Modeling for Thermal Stresses Developed in Riveted and Rivet-Bonded Joints Essam A. Al-Bahkali Abstract A three-dimensional finite element modeling is developed using ABAQUS software. This includes riveted and rivet-bonded joints models. Both models undergo thermal heat caused by hot-driven rivet process and then are subjected to a constant velocity at one of its strip edges to simulate the shear tensile test up to the failure point. The developed FE models were based on elastic-plastic properties and ductile fracture limit criteria. In addition, the adhesive layer was modeled based on traction separation. Detailed experiments were conducted to evaluate these material properties and provide the FE developed models with these necessary data. The thermal stresses developed in riveted and rivet-bonded joints are assessed and reported. The present work shows that introducing an adhesive layer to riveted joints vastly reduces the stresses developed in these joints. In addition, the complete load-displacement curve for each joining model is obtained and compared with the finite element models without including the effect of thermal analysis. Index Term Adhesive Layer, Load-Displacement Curve, Rivet, Rivet-Bonded, Thermal Stresses. I. INTRODUCTION Rivets are used in many design applications such as joining together two plates. A full understanding of these joints is essential in most of automobile and aerospace industries. When a rivet is heated before being placed in the hole, it is identified as hot-driven rivet. After the rivet colds, it presses the connected parts strongly and the rivet pole expands to fill the hole. Thus, the rivet head becomes under high concentration of stresses, which the rivet has to resist. The sharp corner beneath the head may cause the head to be failed. Tearing between the rivet holes, shearing, or crushing of the rivet and/ or the joined material are considered to be the major tension connection failures. Using an adhesive material as bonding is another way of joining two different parts. It is used to adhere a wide range of materials structure such as metal to metal or metal to non-metal. It has the advantages of reducing stress concentration, resisting fatigue, and the capability of joining two different thickness materials as well as joining two dissimilar materials. Bonded structure could be used alone or together with a mechanical This work was supported by College of Engineering Research Center, King Saud University. Essam A. Al-Bahkali is with the Mechanical Engineering Department, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia (phone: ; fax: ; ebhkali@ksu.edu.sa). connection. The bonded with a mechanical connection type may include weld-bonded and rivet-bonded connections. Barron [1] investigated the effect of clamping forces and grip on the fatigue strength of rivets in butt joints. Hoffer [2] determined the load-bearing capacity of a riveted joint by using statistical analysis. He also evaluated the type of the joint failures. Schvechkov [3] studied experimentally the effects of adhesive mechanical properties along with the geometry of butted sheets on the point of failure and cycle longevity on rivet-bonded joints. Fung and Smart [4] examined countersunk and snap riveted single lap joints experimentally and numerically. They studied the failures metallurgically to determine the cause of failure and then they analyzed the joints using the finite element method. They found that the stress concentration for this joint occurred at a point away from the point of failure of a riveted joint. They also determined the stress patterns around the rivet. Bedaira and Eastaugh [5] proposed a numerical procedure for the analysis of riveted lap joints taking into account the effect of the secondary out of plane bending and plates/rivet interaction. Their results showed that the secondary bending largely affects the maximum tensile and compressive stresses within the joint with difference might reach up to 39%. They also presented an experimental comparison using photo-elastic test. Gomeza et al. [6] presented a mechanical model to reproduce the behavior of a structural hybrid adhesive/riveted single lap joint. They used the Bond-Graph technique in order to obtain the equations of the model. These equations depended on four parameters considered to be the characteristics of the joint. Their model reproduced the experimental curves with great precision. Sadowski et al. [7] carried out an experimental investigations of steel adhesive double lap joints reinforced by rivets. They monitored the deformation process of the hybrid joint using digital image correlation system. They also studied the model numerically and analyzed the whole model behavior up to failure point. They found that adding a rivet to the adhesive joint led to very significant energy absorption by about 35% in comparison to a simple adhesive. Moroni et al. [8] evaluated the beneficial of using hybrid weld-, rivet- or clinch-bonded joints in comparison with simple adhesive, spot-welded, riveted or clinched joints. They conducted experimental analysis using the design of experiments methodology. The influence of the material, geometrical factors, and environment on static strength, stiffness and energy absorption was assessed through the

2 International Journal of Engineering & Technology IJET-IJENS Vol: 11 No: analysis of variance. They compared the hybrid and simple joints in terms of mechanical response under the various conditions tested. Al-Bahkali [9] developed three-dimensional finite element modeling for spot welded and weld-bonded joints models for austenitic stainless steel AISI 304 annealed condition sheets of 1.0 mm thickness. In his studied, each model underwent thermal heat caused by spot welding process and then was subjected to an axial load up to the failure point. He defined the properties of elastic and plastic regions, fracture limit, weld nugget and heat affected zones around the spot welding. He also obtained the load-displacement curve for each joining model theoretically and experimentally. The results obtained for both spot welded and weld-bonded joints affected by thermal process showed an excellent agreement with the experimental data. Although several studies on riveted joints have been carried out, however, these studies focused on the failure and strength at room temperature. In the present work, three-dimensional finite element analysis is considered to calculate the thermal stresses caused by hot driven rivet for both riveted and rivetbonded models. In addition, the stress distribution for each model at certain load is determined. Finally, the loaddisplacement curves for both models with and without including the effect of thermal analysis are calculated and compared. II. MODEL A. Geometry The art of the finite element (FE) analysis lies in the representation of a real structure and its loading by a mathematical model, which can be analyzed by the particular analysis program used. An accurate and efficient idealization can be as similar as possible to the real structure from the geometric and loading view points. Two finite element models are considered in the present work. The considered models are a single lap riveted model and a single lap hybrid rivet-bonded model. Fig. 1 shows the configurations, dimensions, constraints, and loading conditions for both models (riveted and rivetbonded models). Throughout the analysis, the following assumptions are considered: 1) The analysis is based on three dimensional FE model. 2) Each model is subjected to thermal analysis, then to an elastic analysis. During the thermal analysis, the hot driven rivet is assumed to be at 160 o C uniform temperature, then it cools until it reaches room temperature. During the elastic analysis, both models are subjected to a constant Velocity that the model is subjected to at the right edge of the right strip to simulate the shear tensile test. 3) A thin isotropic adhesive layer is considered. 4) The line of action force is not initially parallel to the adhesive layer. Thus, as the load increases the overlap area bends and therefore the adhesive layer peel at its ends. Fig. 1. (a) Riveted, and (b) Rivet-Bonded Models B. Finite Element Mesh The finite element computation is carried out using ABAQUS software [10]. Fig. 2 shows the FE mesh for a portion of the hyper rivet-bonded model. Fig. 2. 3D partial finite element mesh of Rivet-Bonded Model The selection of the mesh size is based on the ability to represent each model accurately and obtaining the results in reasonable time. The element type is specified based on the ability to represent the variation of temperature and the mechanical behavior of the model. Therefore, the meshes for

3 International Journal of Engineering & Technology IJET-IJENS Vol: 11 No: each model are generated using eight-node trilinear displacement and temperature reduced integration with hourglass control (C3D8RT) for the strips and rivet, and three dimensional cohesive elements type (COH3D8) for the adhesive layer. The numbers of elements for both models that are used in the current study after several refined meshes to insure the conversion of FE results, are given in Table I. TABLE I Elements number used in different models Model Riveted Model Rivet-Bonded Model Strip A Strip B Adhesive Layer Rivet C. Model Analysis In this research, the analysis of each model is divided into two stages. These stages are thermal analysis and elastic analysis. In the thermal analysis (first stage), stresses caused by cooling the rivet from 160 o C to room temperature are determined. In the elastic analysis (second stage), each model is subjected to a constant velocity (V) at the right edges of strip (B). Out of this analysis, the stresses at certain load and the load-displacement curves are determined for each model. Fig. 3 shows the basic algorithm steps for the analysis models. Where T i is initial temperature, T o is the room temperature, V is the velocity that the model is subjected to at the right edge to simulate the shear tensile test, and h air is the convection heat transfer coefficient. Fig. 3. The basic algorithm steps for the analysis model D. Boundary Conditions 1. Thermal Boundary Conditions A heat transfer analysis is preformed first to cool the rivet part until it reaches room temperature. This can be done by considering a convection heat transfer process as a thermal boundary condition. Hence, it is assumed that heat is exchanged with the environment through a convection heat transfer coefficient h air as: ( ) (1) 2. Elastic Boundary Conditions The mechanical boundary conditions associated with each finite element model can be summarized as the following: 1) On the left edges at x = 0, clamped boundary conditions are imposed. Thus, the displacements u x, u y, and u z are equal to zero. 2) Both strips are subjected to a fixed y-direction boundary condition (u y = 0) at the beginning 30 mm segment of strip A (x = 0 to 30mm) and at the end 30mm segment of strip B (x = 145 to 175mm). 3) In the overlap area for the rivet-bonded model, tie constraints are imposed between components of bonded joints; i.e. both strips and adhesive layer. By doing so, the translational and rotational boundary conditions of tied surfaces are made identical, regardless of the way these parts are meshed. 4) The model is subjected to a constant velocity (V = 1 mm/min.) at the right edges of right base metal strip to simulate the shear tensile test. E. Material Properties Detailed experiments were conducted to evaluate the material properties and provide the FE developed models with these necessary data. These data are given in Table 2. The ductile fracture limits are also defined in terms of stress triaxiality and corresponding equivalent strain for steel [11-17]. The corresponding equivalent strain is obtained from the tensile test of notched specimen and the stress triaxiality is evaluated using numerical simulation [18-19]. The adhesive layer is defined based on traction separation mode. TABLE II Material properties for steel and adhesive Material Adhesive Steel Young s Modulus (GN/m 2 ) Possion s Ratio, Yield Stress S y (MPa) Ultimate Stress S ut (MPa) Specific heat (J/kg o C) Thermal expansion ( C -1 ) Thermal conductivity (W/m o K) III. RESULT The results of riveted and rivet-bonded FE simulations including both thermal and elastic analyses are determined. At first, the stresses resulted from thermal analysis are obtained. Secondly, the stresses at certain load during the elastic analysis are determined. Finally, the load-displacement curves

4 International Journal of Engineering & Technology IJET-IJENS Vol: 11 No: are obtained and compared with the same models but without including the thermal analysis which reflect the case of colddriven rivet A. Thermal stress The results of riveted and rivet-bonded FE models after running thermal analysis are determined and shown in Fig. 4 and Fig. 5, respectively. Both FE models undergo a heat transfer analysis until they reach room temperature starting from temperature T i =160 o C. Mises stress ( V.M ). While the normal stress x has high stress concentration underneath the rivet head and in contact with the strips edges at the top and bottom of the rivet hole as shown in Fig. 4-(a), the normal stress y has high stress at the rivet center and in contact with the strips as shown in Fig. 4-(b). On the other hand, the shear stress contour (see Fig 4-(c)) illustrates that the high stress level (tension and compression) takes a diagonal shape starting from the contact edge between strips and underneath the rivet head toward the surface of the rivet head. Fig. 4. Thermal Stress Contours for Riveted Model Fig. 4 shows the contour plots for riveted model for the normal stresses ( x & y ), the shear stress ( xy ), and the Von Fig. 5. Thermal Stress Contours for Rivet-Bonded Model

5 International Journal of Engineering & Technology IJET-IJENS Vol: 11 No: Fig. 4-(d) shows the combined contour stress ( V.M ) developed in riveted joint. It can be seen that the rivet head becomes under high concentration of stresses, which the rivet has to resist. The locations of these stresses are at the sharp corner beneath the head and the areas in contact with the edges of both strips. Fig. 5 shows the stress contour plots x, y, xy, and V.M for rivet-bonded model. Although the pattern of the stress contours is similar to the contours in Fig 4, however, the level of stresses is very small. This is because of the addition of the adhesive layer between the strips joint. Again, the combined contour stress ( V.M ) as shown in Fig. 5-(d) demonstrates that the rivet head becomes under high stress concentration at the sharp corner beneath the head and in contact with the edges of both strips. B. Stress distribution at certain applied load During the elastic FE simulation, it is very important to study the stress distribution at the overlap area. Therefore, a load of 3000N is applied while the model is still running in the elastic region. This is done for both riveted and rivet-bonded models. Stresses Developed in Riveted Joint Model The predicted stresses (σ xx, σ yy and σ xy ) along with σ V.M stress through the mid-layer area of the jointed area are shown in Figs. 6 and 7. Fig. 6 demonstrates the stresses developed in the longitudinal direction, where the shear stress σ xy is dominating the rest of the stresses (σ xx and σ yy ). The stress σ yy is near zero. The figure also shows that the longitudinal σ V.M takes its minimum value (37.6MPa) at the center of the rivet and rapidly reaches its maximum value (356.6MPa) at the far ends of the rivet. Fig.7 shows the stresses developed in the transverse direction. As can be seen from the figure, the shear stress σ xy is also dominating the rest of the stresses σ xx and σ yy. The figure shows that the transverse σ V.M stress takes its minimum value (37.6MPa) at the center of the rivet and its maximum value (196.5MPa) at the far ends of the rivet s side. Fig. 7. Transverse stresses (developed in the center overlapped riveted joint along the z-direction). Stresses Developed in Rivet-Bonded Joint Model The predicted stresses for σ xx, σ yy σ xy, and σ V.M stress through the mid-layer of the joined area are shown in Fig. 8 and Fig. 9. Fig. 8 displays the stresses developed in the longitudinal direction. It is seen that the stress σ xx is dominating the rest of stresses. The stress σ yy is nearly of zero value. The figure also shows that the longitudinal σ V.M stress takes several local minimum and maximum values across the joint area. In the rivet area, the local minimum value occurs at the center of the rivet with a value of 66.4MPa while the maximum value takes places at the far ends of the rivet with a value of 131.8MPa. Fig. 9 demonstrates the stresses developed in the transverse direction, with σ xx being also the dominant stress. The figure also shows that the transverse σ V.M stress for the rivet takes its minimum value at the center of the overlap area and its maximum value at the rivet s side with a value of 144.6MPa. Fig. 6. Longitudinal stresses (developed along the mid-layer of overlapped riveted joint). Fig. 8. Longitudinal stresses (developed along the mid-layer of overlapped rivet-bonded joint).

6 International Journal of Engineering & Technology IJET-IJENS Vol: 11 No: Fig. 9. Transverse stresses (developed in the center overlapped rivetbonded joint along the z-direction). Figs. 8 and 9 show that the Von Mises stresses developed in rivet-bonded joints are nearly of low and uniform value compare to the riveted model. They also show that the V. M. stresses of riveted joints are reduced by 63% in the longitudinal direction and by 26.4% in the transverse direction when the adhesive layer is introduced. C. Load-displacement Curve The results of riveted and rivet-bonded FE simulations including the effect of thermal analysis are determined. The results are compared with the same FE models but without including the effect of the thermal analysis. Fig. 10 shows four load-displacement curves obtained from the FE riveted and rivet-bonded models. These four curves are: riveted model runs at room temperature, riveted model runs at temperature T i =160 o C, rivet-bonded model runs at room temperature, and rivet-bonded model runs at temperature T i =160 o C. By comparing all curves, it is clear that both riveted models with and without including the effect of thermal analysis have the same trend. However, for the riveted model with thermal analysis, the maximum load is increased by 9% and the displacement is increased by 25%. Similarly, both rivet-bonded models with and without including the effect of thermal analysis are alike in general, but the maximum load and displacement of the rivet-bonded model with thermal analysis are increased by almost the same amount of 9% and 23%, respectively. By comparing the trend of the obtained load-displacement curves with other pervious published work such as Birch et al. [20], these curves show, in general, a very good agreement with their results. IV. SUMMARY AND CONCLUSION A three-dimensional FE riveted and rivet-bonded models are developed. Both models undergo thermal analysis caused by hot-driven rivet and then are subjected to a constant velocity at one of its strip edges to simulate shear tensile test. The two-step analysis is used to include the effect of residual stresses cased by high initial temperature. In addition, stresses at certain load and load-displacement curve for each joining model are successfully obtained. The results show that introducing the adhesive layer to riveted joints increases the joint strength and significantly reduces the stresses developed in riveted joints. It is found that, adding the thermal analysis to the solution seems to have an effect on the steel structure. During the cooling cycle from T i =160 o C to room temperature, carbides precipitate more uniformly throughout the steel structure which improves the strength by at least 9% and the displacement by 23%. The analysis in this paper has been executed by running the Abaqus/Standard procedure. To fully understand the dynamic behavior of the joints and the failure modes, this study can be extended by running Abaqus/Explicit procedure to include the time-domain in the analysis. This will help investigating the influences of different parameters on riveted and rivet-bonded joints such as the sensitivity of the strain rate and the fracture limits. It is recommended to carry out some experimental works to verify the results. Fig. 10 Load-displacement curves for rivet and rivet-bonded models with or without including the thermal analysis. REFERENCES [1] K. Hoffer, Rivet Joints in Aluminum Structural components I and II Aluminum, p. 391, p. 473, [2] F. Barron and E. W. Larson, Comparison of Bolted and Riveted Joints, Trans. Am. Soc. Civil Eng., 1955, pp [3] E. I. Schvechkov, Failure Patterns and Cycle Longevity of Rivet-Bonded Joints, Masinovedenie, 1984, p. 71.

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